Drinfeld modular polynomials in higher rank II: Kronecker congruences

2013/03/17 by Florian Breuer, Breuer, Florian, Hans-Georg Rück +1 · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1303.4086

Abstract

This is a sequel to the paper [F. Breuer, H.-G. Rück, Drinfeld modular polynomials in higher rank, J. Number Theory 129 (2009), 59-83.], in which we introduced Drinfeld modular polynomials of higher rank, using an analytic construction. These polynomials relate the isomorphism invariants of Drinfeld F_q[T]-modules of rank r≥ 2 linked by isogenies of a specified type. In the current paper, we give an algebraic construction of greater generality, and prove a generalization of the Kronecker congruences relations, which describe what happens when modular polynomials associated to P-isogenies are reduced modulo a prime P. We also correct an error in [loc. cit.].

Cited by

• CM Drinfeld Modules, Self-isogenous Modular Polynomials, and Volcano Structure

Related

• Drinfeld Modular Polynomials in Higher Rank
• Drinfeld modular polynomials of level T
• The generic monodromy of Drinfeld modular varieties in special\n characteristic
• CM Drinfeld Modules, Self-isogenous Modular Polynomials, and Volcano Structure
• Explicit description of isogeny and isomorphism classes of Drinfeld\n modules over finite field